a real world point of view
The supervising sound editor or sound supervisor is in charge of the entirety of post-production sound. They lead the team tasked with assembling the soundtrack for an episode as it moves through the editing process.
In the earliest days of Doctor Who's production history, such a position did not exist because there was practically no post-production of any kind during the William Hartnell and Patrick Troughton eras. Even into the 1970s and 1980s, the notion of having genuine post-production sound — ADR, foley and the like — was unusual. Generally, whatever the microphones picked up during principal photography formed the bulk of the soundtrack.
Starting with the 1996 telemovie, Doctor Who adopted a more American form of production, and the role of post-production sound became more obvious. During the BBC Wales run, the most common supervising sound editor was Paul McFadden, but Doug Sinclair and Walt Newman both held the position at Torchwood.